Social groups in a population can lend important cues to law enforcement officials, consumer-based services and risk assessors. Social and geographical patterns that provide information about such communities or gangs have been a popular subject for mathematical modeling. Scientists used police department records about individuals' social and geographical information to determine gang memberships.

Social groups in a population can lend important cues to law enforcement officials, consumer-based services and risk assessors. Social and geographical patterns that provide information about such communities or gangs have been a popular subject for mathematical modeling.

Related Articles

In a paper published last month in the SIAM Journal on Applied Mathematics,authors use police department records about individuals' social and geographical information to determine gang memberships.

Data on social interactions is particularly hard to come by, but in combination with geographical data, it can determine locations of specific groups in the population, such as gangs. For instance, if an individual's geographic location at a set of times is known, social interactions may be inferred by detecting people present at the same place at the same time. In this manner, hotspots at major gang locations can be determined.

In this paper, data is used from LAPD field interview cards, which document stops by police officers of known or suspected gang members in the Hollenbeck area of Los Angeles. For each of the 748 gang members whose data is compiled, the average of all locations where they were stopped is determined, in addition to other individuals that may have been present at each stop. Due to the generally nonviolent nature of the stops, individuals stopped together are assumed to share a friendly or social connection.

A fully connected graph is constructed using this information with nodes that represent 748 individuals and an associated affinity matrix. An affinity matrix helps determine the similarity or likeness between two sets of objects or parameters. The matrix is a combination of social adjacency and an encoding function that depends on the average stop distances between individuals. In order to cluster the individuals, the authors use a technique called spectral clustering, a mathematical method used to identify groups of "similar behavior" in data. This identifies clusters in the graph based on the above-mentioned social connections.

"One thing our study shows is that a clustering based purely on the locations where the people were stopped already provides clusters of over 50% purity, indicating the important role that geography plays," says lead author Yves van Gennip.

A greater amount of social data leads to improvements in clustering metrics. Since social data for such studies tends to be low, social information is extended past the current levels of sparsity by augmenting it with noise and available data on connections between members of the same gang. Such extensions of data can be particularly advantageous in tightly-controlled security settings, such as war zones. For instance, in the border regions of Afghanistan, taking into account familial, tribal and religious affiliations as well as social and economic concerns of individuals can help identify their support for insurgencies -- active or passive. While intelligence information from the ground can be meager in such areas, meetings of groups of individuals can be easily observed. These methods can also be used to establish social, and hence, group interactions through geosocial information available from social media sites.

"The type of analysis undertaken in the paper can have practice applications for local law enforcement," explained one of the authors, George Tita. "While it certainly will not provide clues as to the particular individual that committed a gang-motivated crime, it can provide investigators a starting point with respect to the particular gang that might have been involved in the attack. Thus, the results of our analysis can provide a way for local police to allocate their scarce resources more strategically."

Including both social and geographic distance in models of gang violence such as this is seen to provide more comprehensive analysis -- for example, in ecological models, even low levels of competition between gangs can produce sharp boundaries between gangs with a pattern of violence along borders. This "sociospatial" dimension can thus allow successful intervention to reduce gang violence. Targeted enforcement is seen not only to reduce crime in the area surrounding a gang, but also to diffuse through social networks, reducing violence among gang rivals.

"We are currently working on a much larger dataset that is similar to the one discussed in the paper," said Andrea Bertozzi, one of the authors. "The challenge is to develop algorithms that will use raw data from field interview cards from tens of thousands of people over several-years worth of events."

More From ScienceDaily

More Computers & Math News

Featured Research

Mar. 3, 2015 — By examining the forces that the segments of mosquito legs generate against a water surface, researchers have unraveled the mechanical logic that allows the mosquitoes to walk on water, which may ... full story

Mar. 3, 2015 — Major cities in the UK are falling behind their international counterparts in terms of their use of smart technologies, according to a new study. The research has found that smart cities in the UK, ... full story

Mar. 3, 2015 — To simulate chimp behavior, scientists created a computer model based on equations normally used to describe the movement of atoms and molecules in a confined space. An interdisciplinary research ... full story

Mar. 3, 2015 — Magnetic vortex structures, so-called skyrmions, could in future store and process information very efficiently. They could also be the basis for high-frequency components. For the first time, a team ... full story

Mar. 2, 2015 — The odds of picking a perfect bracket for the NCAA men's basketball March Madness championship tournament are a staggering less than one in 9.2 quintillion (that's 9,223,372,036,854,775,808), ... full story

Mar. 2, 2015 — Scientists report that they could observe experimentally the current flow along channels at the crystal surfaces of topological insulators. The channels are less than one nanometer wide and extend ... full story

Mar. 2, 2015 — Organic light emitting diodes (OLEDs), which are made from carbon-containing materials, have the potential to revolutionize future display technologies, making low-power displays so thin they'll wrap ... full story

Mar. 2, 2015 — What if one day, your computer, TV or smart phone could process data with light waves instead of an electrical current, making those devices faster, cheaper and more sustainable through less heat and ... full story

Mar. 2, 2015 — 3-D printing could become a powerful tool in customizing interventional radiology treatments to individual patient needs, with clinicians having the ability to construct devices to a specific size ... full story

Featured Videos

Forensic Holodeck Creates 3D Crime Scenes

Reuters - Innovations Video Online (Mar. 3, 2015) — A holodeck is no longer the preserve of TV sci-fi classic Star Trek, thanks to researchers from the Institute of Forensic Medicine Zurich, who have created what they say is the first system in the world to visualise the 3D data of forensic scans. Jim Drury saw it in operation.
Video provided by Reuters

Sep. 24, 2014 — Although membership in a gang often is depicted as a lifelong commitment, the typical gang member joins at age 13 and only stays active for about two years, according to a ... full story

July 26, 2013 — Gang members trust one another more than their own family members if they have shared incriminating information about a violent act they are planning, says a new Oxford University study. Researchers ... full story

June 25, 2012 — A mathematical model that has been used for more than 80 years to determine the hunting range of wild animals holds promise for mapping the territories of street gangs, social scientists report. The ... full story

Oct. 31, 2011 — Mathematicians working with the Los Angeles Police Department to analyze crime patterns have designed a mathematical algorithm to identify street gangs involved in unsolved violent crimes -- the ... full story

ScienceDaily features breaking news and videos about the latest discoveries in health, technology, the environment, and more -- from major news services and leading universities, scientific journals, and research organizations.